Finite Group DatabasebetaFinite Group Databasebeta| order | 6090 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D7×C29 |
| Fitting, socle, Hall | C3×C5×C7×C29 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C3×C5×C29 |
| Hall | C5×C7×C29 ⋊ C2×C3 |
| Hall | C3×C7×C29 ⋊ C2×C5 |
| Hall | C7×C29 ⋊ C2×C3×C5 |
| Hall | C3×C5×C7 ⋊ C2×C29 |
| Hall | C5×C7 ⋊ C2×C3×C29 |
| Hall | C3×C7 ⋊ C2×C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C29 | D7 |
| commutator, hypocenter | C7 | C2×C3×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C29 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C5×C29 | |
32 conjugacy classes of subgroups.
2175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6090, 5);